Question: Gabriela is 2 times as old as Jessica. 30 years ago, Gabriela was 7 times as old as Jessica. How old is Jessica now?
Solution: We can use the given information to write down two equations that describe the ages of Gabriela and Jessica. Let Gabriela's current age be $g$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $g = 2j$ 30 years ago, Gabriela was $g - 30$ years old, and Jessica was $j - 30$ years old. The information in the second sentence can be expressed in the following equation: $g - 30 = 7(j - 30)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to use our first equation for $g$ and substitute it into our second equation. Our first equation is: $g = 2j$ . Substituting this into our second equation, we get: $2j$ $-$ $30 = 7(j - 30)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $2 j - 30 = 7 j - 210$ Solving for $j$ , we get: $5 j = 180.$ $j = 36$.